CN104613942B - Analytic method of image pair relative elements of exterior orientation - Google Patents

Abstract

The invention discloses an analytic method of image pair relative elements of exterior orientation. The analytic method is characterized by comprising the following steps: selecting two points with proper distance on a vertical direction, respectively shooting on the two points to obtain an upper image S1 and a lower image S2 to construct a group of image pair, wherein the upper image S1 is used as a standard image; knowing the elements of interior orientation of two images as f, ui0, vi0, ui0' and vi0'; computing to obtain corrected image collimation mark coordinate (ui, vi) of S1 and the corrected image collimation mark coordinate (ui', vi') of the S2; and then respectively selecting three corresponding image points (i equals to 1, 2, 3) on the S1 and S2, solving the relative elements of exterior orientation bx, by, bz, phi, Kappa and parameter lambda of the image pair.

Description

A kind of analytic method to elements of exterior orientation relatively for picture

First, technical field

The method belong in close-range photogrammetry using as to the elements of interior orientation method that solves relatively elements of exterior orientation.

2nd, technical background

In close-range photogrammetry, elements of exterior orientation is to determine light beam position in given object space coordinate system d-xyz Key element with direction.Elements of exterior orientation has six, three exterior orientation vertical elements and three foreign side's parallactic angle elements.Three foreign sides Position vertical element, i.e. coordinate figure (x_s, y_s, z_s), in order to describe light beam summit (photo centre) s in object space coordinate system d-xyz In position；Three foreign side's parallactic angle elements (κ, ω), in order to describe direction in object space coordinate system d-xyz for the light beam.

Image space coordinate system s-xyz rotates three angles through orderObtain space auxiliary coordinates s- Xyz, whereinω, κ be respectively picture point in image space coordinate system s-xyz around y-axis, x-axis, z-axis the anglec of rotation.

3rd, content of the invention

A kind of picture to the analytic method of relatively elements of exterior orientation it is characterised in that: in the vertical direction chooses suitable distance 2 points, and photography obtains upper piece s respectively on this 2 points₁With bottom sheet s₂, constitute one group of picture pair, wherein above piece s₁For standard Photo；The elements of interior orientation of known two photos is f, u_i ⁰, v_i ⁰, u_i ^0’, v_i ^0’；S is tried to achieve in calculating₁Fiducial mark of the photograph coordinate after correction (u_i, v_i), s₂Fiducial mark of the photograph coordinate (u after correction_i', v_i’)；Then in photo s₁、s₂3 corresponding image points of upper selection respectively are (i.e. I=1,2,3), two photo s are obtained by close-range photogrammetry knowledge₁And s₂Between relational expression:

$r\left(\begin{array}{c}{u}_i^{\′}\\ f\\ v_i^{\′}\end{array}\right)-{\mathrm{\λ}}_i\left(\begin{array}{c}{u}_i\\ f\\ v_i\end{array}\right)-\begin{array}{}\end{array}\left(\begin{array}{c}{b}_x\\ b_y\\ b_z\end{array}\right)=0$

Wherein, r is spin matrix；λ_i, r_i, r_i' it is zoom factor；b_x, b_y, b_zRepresent three exterior orientation vertical elements respectively x_s, y_s, z_sKnots modification δ x_s, δ y_s, δ z_sWith zoom factor r_i' between relation.

${\mathrm{\λ}}_i=\frac{r_i}{{r_i}^{\′}}$ $\left(\begin{array}{c}{b}_x\\ b_y\\ b_z\end{array}\right)=\frac{1}{{r_i}^{\′}}\left(\begin{array}{c}\mathrm{\δ}{x}_s\\ {\mathrm{\δy}}_s\\ \mathrm{\δ}{z}_s\end{array}\right)$

Finally choose 3 corresponding image points, solve as to relative elements of exterior orientation bx, by, bz,ω, κ and parameter lambda:

$\underset{3\·7}{a}\underset{7\·3}{x}+\underset{3\·1}{b}=\underset{3\·1}{o}$

Wherein a is coefficient matrix；X is parametric array to be asked；B is constant.

$\begin{array}{cc}a=\left(\begin{array}{ccccccc}-f& 0& -v_i^{\′}& -u_i& -1& 0& 0\\ u_i^{\′}& -v_i^{\′}& 0& -f& 0& -1& 0\\ 0& f& u_i^{\′}& -v_i& 0& 0& -1\end{array}\right)& b=\left(\begin{array}{c}{u}_i^{\′}\\ f\\ v_i^{\′}\end{array}\right)\end{array}$

The inventive method has the advantage that

Constitute one group of picture pair with two photos of vertical direction photographs, in the situation of known two elements of interior orientation Under, choose 3 corresponding image points, calculate elements of exterior orientation and this seven parameters of zoom factor.

4th, brief description:

Further illustrate below in conjunction with the accompanying drawings and to this method.

Fig. 1 is the internal and external orientation schematic diagram of photo.Wherein, d-xyz is object space coordinate system, and s-xyz is as empty Between coordinate system, s-xyz be space auxiliary coordinates,κ, ω are three anglecs of rotation, and s is photo centre, away from x based on f_s、y_s、 z_sFor three exterior orientation vertical elements.

Fig. 2 is photo schematic diagram.Wherein, (a) represents photo s₁And s₂Collimation mark coordinate system；Two pictures when () represents photography b The relative position of piece.

5th, specific embodiment:

1st, in the vertical direction chooses 2 points of suitable distance, and photography acquisition upper piece s respectively on this 2 points₁And bottom sheet s₂, constitute one group of picture pair, wherein above piece s₁For standard photo；

2nd, the elements of interior orientation according to two photos is f, u_i ⁰, v_i ⁰, u_i ^0’, v_i ^0’, calculate and try to achieve s₁Photo frame after correction Mark coordinate is (u_i, v_i), s₂Fiducial mark of the photograph coordinate after correction is (u_i', v_i’)；

3 and then in photo s₁、s₂Upper 3 corresponding image points of selection respectively, obtain two according to close-range photogrammetry knowledge solution Photo s₁And s₂Between parsing relation；

4th, finally choose 3 corresponding image points, solve as to relative elements of exterior orientation bx, by, bz,ω, κ and parameter λ.

Claims (1)

1. a kind of picture to the analytic method of relatively elements of exterior orientation it is characterised in that: in the vertical direction chooses suitable distance 2 points, and photography acquisition upper piece s respectively on this 2 points₁With bottom sheet s₂, constitute one group of picture pair, wherein above piece s₁For official portrait Piece；The elements of interior orientation of known two photos is f,S is tried to achieve in calculating₁Fiducial mark of the photograph after correction is sat Mark (u_i, v_i), s₂Fiducial mark of the photograph coordinate (u after correction_i', v_i’)；Then in photo s₁、s₂Upper 3 corresponding image points of selection respectively, Corresponding i=1,2,3, two photo s are obtained by close-range photogrammetry knowledge₁And s₂Between relational expression:

$r\left(\begin{array}{c}{u}_i^{\′}\\ f\\ v_i^{\′}\end{array}\right)-{\mathrm{\λ}}_i\left(\begin{array}{c}{u}_i\\ f\\ v_i\end{array}\right)-\left(\begin{array}{c}{b}_x\\ b_y\\ b_z\end{array}\right)=o$

Wherein, r is spin matrix；λ_i, r_i, r_i' it is zoom factor；b_x, b_y, b_zRepresent three exterior orientation vertical element x respectively_s, y_s, z_sKnots modification δ x_s, δ y_s, δ z_sWith zoom factor r_i' between relation；

Finally choose 3 corresponding image points, by following formula solve as to relative elements of exterior orientation bx, by, bz,ω, κ and ginseng Number λ:

Ax+b=o

Wherein a is coefficient matrix；X is parametric array to be asked；B is constant,

$\begin{array}{cc}a=\left(\begin{array}{ccccccc}-f& 0& -v_i^{\′}& -u_i& -1& 0& 0\\ u_i^{\′}& -v_i^{\′}& 0& -f& 0& -1& 0\\ 0& f& u_i^{\′}& -v_i& 0& 0& -1\end{array}\right)& b=\left(\begin{array}{c}{u}_i^{\′}\\ f\\ v_i^{\′}\end{array}\right)\end{array}$